I am trying to write my first trigger on a sql server 2008 r2 database.I keep getting a procedure error the 'INSERT INTO [dbo].[RPT_Trans_Audit] (Package_ID, Received_Date, Download_Date)' statement listed below. I do not know what is wrong. Can you tell me what I need to change?

If the reason you are doing this is to ensure atomicity of the operations, you should add a begin tran and end tran also, and handle the transaction appropriately. There are two very good examples on this MSDN page, examples B and C: http://msdn.microsoft.com/en-us/library/ms175976.aspx

You should also be aware that if you rollback a transaction in the trigger, that will cause rollback of the insert/update/delete that triggered the transaction.